5 people can paint 7 walls in 32 minutes. How many minutes will it take for 9 people to paint 8 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 5\text{ people}\\ t &= 32\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{32 \cdot 5} = \dfrac{7}{160}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 9 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{7}{160} \cdot 9} = \dfrac{8}{\dfrac{63}{160}} = \dfrac{1280}{63}\text{ minutes}$ $= 20 \dfrac{20}{63}\text{ minutes}$ Round to the nearest minute: $t = 20\text{ minutes}$